3(x-9)(x-7)-(x-7)(x-9)=0

Solution for 3(x-9)(x-7)-(x-7)(x-9)=0 equation:

3(x-9)(x-7)-(x-7)(x-9)=0

We multiply parentheses ..

3(+x^2-7x-9x+63)-(x-7)(x-9)=0

We multiply parentheses

3x^2-21x-27x-(x-7)(x-9)+189=0

We multiply parentheses ..

3x^2-(+x^2-9x-7x+63)-21x-27x+189=0

We add all the numbers together, and all the variables

3x^2-(+x^2-9x-7x+63)-48x+189=0

We get rid of parentheses

3x^2-x^2+9x+7x-48x-63+189=0

We add all the numbers together, and all the variables

2x^2-32x+126=0

a = 2; b = -32; c = +126;
Δ = b2-4ac
Δ = -322-4·2·126
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4}{2*2}=\frac{28}{4}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4}{2*2}=\frac{36}{4}
=9
$